Introduction of Fourier Series to First Year Undergraduate Engineering Students

Transcription

1 Itertiol Jourl of Adved Reserh i Computer Egieerig & Tehology (IJARCET) Volume 3 Issue 4, April 4 Itrodutio of Fourier Series to First Yer Udergrdute Egieerig Studets Pwr Tejkumr Dtttry, Hiremth Suresh Shivrudrpp *, Birjdr Gj Mlleshi, Bhople Ashwikumr Aru Brhmdevdd Me Istitute of Tehology, Solpur (Mhrshtr), Idi Astrt: I this pper we hve itrodued the geerl form of Fourier series to simplify the etter uderstdig of the oept of Fourier expsio of futios. Keywords: Cosie series, Egieerig studet, Fourier expsio, Sie series. Itrodutio: For first yer udergrdute egieerig studets it is quite diffiult to rell the results of Fourier series for give exmple. Beuse lmost i ll the ooks of egieerig mthemtis umer of results re defied itervl wise. For exmple (,, ) (, ) (, ), (, ), (, ),(, ),(,) (,, ) et. Usully my studets get ofuse out the seletio of the results. The form whih we hve itrodued here e used to fid the Fourier expsio of futio for y give itervl. Our ttempt is to itrodue the Fourier series to first yer udergrdute egieerig studets i suh wy tht they esily oti the Fourier expsio for give futio i y itervl without y ofusio d memorize the miimum umer of formule. Geerl Formul for Fourier Series: It is ot eessry to rell ll set of formule, it is suffiiet to rememer oly three formule give elow. ) Fourier series for futio i (, ) whih is stted elow ( x os x si ), x os d x si ) Hlf rge osie series i (,): x os ISSN: x os All Rights Reserved 4 IJARCET 3

2 Itertiol Jourl of Adved Reserh i Computer Egieerig & Tehology (IJARCET) Volume 3 Issue 4, April 4 d 3) Hlf rge sie series i (,): x si x si Aove results e overted to y suitle give itervl d for tht studets re dvised to uderstd the followig thigs for give prolem. ) To deide whether result, or 3 is suitle tht depeds upo questio. ) Uderstd (ower limit) 3) Uderstd U (Upper limit) 4) The vlue of whih e lulted y simple result. Totl legth of geerl itervl = Totl legth of give itervl. Ad mke the hges from, 3, 4 i tht eomes suitle result for give prolem. For exmple: Que ) oti the Fourier series for x ( ) i (, ) Fourier series is expeted so we shll fous o result give elow ( x os x si ) x os d x si ISSN: All Rights Reserved 4 IJARCET 4

3 Itertiol Jourl of Adved Reserh i Computer Egieerig & Tehology (IJARCET) Volume 3 Issue 4, April 4 Here ) = ) U= 3) egth of geerl itervl = egth of give itervl = Hee = Therefore = We shll mke ove three hges t time i ove seleted results. ( os x si x) osx si x Here fter lultio for ove ostts to e mde s usul. Que.) Fid hlf rge osie series for os x i (, ) Fourier series is expeted so we shll fous o result give elow x os x os ISSN: All Rights Reserved 4 IJARCET 5

4 Itertiol Jourl of Adved Reserh i Computer Egieerig & Tehology (IJARCET) Volume 3 Issue 4, April 4 Here ) = ) U= 3) egth of geerl itervl = egth of give itervl = Hee = We shll mke ove three hges t time i ove seleted results i. os x osx Here fter, lultio for ove ostts to e mde s usul. Similrly hlf rge sie series lso e otied. Colusio: For egieerig studets fidig effiiet wy of lerig mthemtis is very importt. To mke their lerig etter mthemtis should e itrodued to them i geerl wy. As they do ot hve suffiiet itetio d time to study mthemtis rigorously. I this pper we hve preseted itrodutio of Fourier series i simple d geerl wy. Egieerig studets will fid this very esy d etter to uderstd the oepts Fourier series. Akowledgemet: The uthors thk the Priipl Dr. M S Pwr for his suggestios d ides tht helped to improve this rtile. Authors Cotriutio: We ll the four uthors hve red this rtile ompletely d we ll hve otriuted eqully towrds the ompletio of this rtile. ISSN: All Rights Reserved 4 IJARCET 6

5 Itertiol Jourl of Adved Reserh i Computer Egieerig & Tehology (IJARCET) Volume 3 Issue 4, April 4 Referees: [] H K Dss, Rjish Verm Higher Egieerig Mthemtis S.Chd, Editio II, [] N P Bli, Ashok Sxe, N Ch S Nry Iyegr A Text ook o Egieerig Mthemtis xmi Pulitio(P) TD. Fourth Editio, [3] Hiremth S S A Alysis of the Tehig d erig of Mthemtis i Udergrdute Egieerig Courses Itertiol Jourl of Busiess, Mgemet d Soil Siees(IJBMS) Vol.II,Issue7(IX),pge o. -, Mrh 3 ISSN: [4] Hiremth S S,Birjdr G M A Differet Approh of Itroduig Bet d Gmm Futio to First Yer Udergrdute Egieerig Studets Mthemtil Siees Itertiol Reserh Jourl, Vol., Issue, pge o , Aug 3 ISSN: [5] J P Khe Fourier Series d Wvelet Mthemtis Uiversity of Pris-Sud Orsy(Fre). ISSN: All Rights Reserved 4 IJARCET 7